The Ankeny-Artin-Chowla congruence is a result in number theory published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla. It concerns the class number of a real quadratic field with positive discriminant, relating it by a congruence modulo a prime to the field's fundamental unit. A related form of the congruence, tied to Bernoulli numbers, holds when the discriminant is itself a prime congruent to one modulo four. The result has since been generalized further by other authors. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementFor a real quadratic field of discriminant d greater than zero, the class number of the field satisfies a stated congruence modulo the field's prime, linking the class number to properties of the field's fundamental unit. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Ankeny-Artin-Chowla congruence (Wikipedia)
Proved By
Source Ankeny-Artin-Chowla congruence (Wikipedia)
Sources
1. Ankeny-Artin-Chowla congruence (Wikipedia)
Lead section
the Ankeny-Artin-Chowla congruence is a result published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla.
- In Branch: Number Theory, Lead sentence
Proved By: Emil Artin, Lead paragraph
In number theory, the Ankeny-Artin-Chowla congruence is a result published in 1953 by N. C. Ankeny, Emil Artin and S. Chowla. It concerns the class number
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